8) Prove by contradiction that, if one rolls a die for 25 times, at least 5 of them must show the same number

Q: 7. On the outside rim of a circular disk the integers from 1 through 30 are painted in random order.…

A: Let us consider all possible sums of three successive integers. For this, suppose, we start with the…

Q: A ballroom is full of people (say more than 200). What is the least number of people that you must…

A:

Q: Die A has four 9's and two 0's on its faces. Die B has four 3's and two 11's on its faces. When…

A: Given information: Die A has four 9's and two 0's on its faces. Die B has four 3's and two 11's on…

Q: In a particular lottery, 6 winning numbers are drawn from a group of 55 numbers. The order that the…

A: Given that, there are total 55 numbers and among them winning numbers are 6.

Q: a)Rolling a sum of 9 on two dice.

A: Dear Student, As per the guideline, I can solve any one question or " its 3 subparts ". kindly…

Q: a coin is tossed 5 times, and then a standard six-sided die is rolled 3 times, and finally a group…

A: A coin tossed 5 times Coin has two outcomes : (H,T) Each toss is differentStandard six sided die is…

Q: In how many ways can a class of 13 students be assigned 2 A's, 2 B's, 4 C's, 3 D's and 2 F's?

A: Number of students in a class .We are asked to find the number of ways to grade of students ().

Q: nhow many nights may a watch of 4 men be arranged by a security agency om a crew of 16 so that no…

A:

Q: An urn contains 12 numbered balls, of which 6 are black, and 6 are white.  A sample of 6 balls is…

A: Number of ways of selecting a sample of 6 balls from 12 balls is given by: 126 = 12!6! x (12-6)!…

Q: 2. Find a) the probability that all 4 people in a group of 4 were born on January 14; b) the…

A:

Q: A bag contains four different balls colored Red, White, Blue, and Green. You cannot see into the bag…

A: If two balls are selected at random without replacement, For permutations, nPr = n!/(n-r)! Now, 2…

Q: The pool of students in a calculus class consist of 22 sophomore and 8 freshmen. If seven students…

A: (a) Determine the number of different groups of seven students can be selected. The number of…

Q: In how many ways can 16 balls be drawn from an urn containing 3 red balls, 8 white balls, and 5 blue…

A: We have given that,  Red balls = 3  White balls= 8  Blue  balls= 5 Then,  We wil find the how many…

Q: What is the probability that a fair six-sided die, rolled 10,000 times, will result in an outcome…

A:

Q: 5) The number of 3 - digit numbers with repeats, that are multiples of 5 and less than 600 that can…

A: A three digit number should be made which is less than 600. The objective is to find the number of 3…

Q: . How many numbers of 5 different digits can be made from the digit 1,2,3,...9? 2. How many numbers…

A:

Q: I have a bucket of n green balls labeled 1, 2, . . . , n. I have another bucket of red balls labeled…

A: The events are occurring simultaneously. So,  Total combinations=combinations for green…

Q: If S = 1+2+4+ 8+ 16+ 32 + 64 + ... + 1024, then S = 2" – 1 where n =

A: Given: ∑r=0602r=2n-1 S=1+2+4+8+16+32+64+...+1024 Then S=2n-1

Q: How many people are needed to guarantee that at least 4 people have a birthday in the same month?

A: This is an application of pigeon hole principle. According to pigeon hole principle, if there are n…

Q: A class has 11 students. What is the probality that exactly 4 of the students were born on a weekday…

A: We have to find given probability.

Q: How many possible outcomes are there if I toss an eight sided die three times?

A: See solution below

Q: Each prize winners will be randomly selected from 25 people attending a party. There will be 1st,…

A: here given there are total 25 people and total 8 prize are there  here use counting Principle

Q: There are n balls in the urn , of which (n-1) balls are marked   with the number 1 , and the last -…

A:

Q: You have 8 pairs of socks of different colours in one of your drawers [a pair has both socks of the…

A:

Q: 2. In the selection of 16 finalists, 3 finalists will be selected to participate in the next round,…

A: It is given that  Total finalist = 16 Selected finalist for next round = 3

Q: a committe of four people is to be chosen from a nine member group to represent the group on an…

A: a committee of four people is to be chosen from a nine member group to represent the group on an…

Q: a) Find the probability of exactly 20 particles arrive in a particular one minute period. b) Find…

A: From provided information, An average of 15 particles per minute occurs, Mean of poisson…

Q: A sequence of resistors or other components wired into a circuit one after the other?

A: A sequence of resistors or other components wired into a circuit one after the other refers to…

Q: n urn contains 12 numbered balls, of which 6 are black, and 6 are white.  A sample of 4 balls is…

A: Total no.of balls  = 12 No.of white balls = 6 No.of black balls = 6 Consider that sample of 4 balls…

Q: We roll 10 different dice, each of which has 12 sides with the numbers 1 through 12 showing on them.…

A: Permutation: A permutation of a set is defined as an arrangement of its members into a sequence or…

Q: A local county has an unemployment rate of 6%. A random sample of 16 employable people are picked at…

A:

Q: 2. In how many ways can five students queue for tickets for a show?

A: The number of ways in which five students queue for tickets for a show is           5!  ways…

Q: 2. In how many ways can a group of 6 women and 5 men line up for a photograph if no two adjacent…

A: There are a total of 6 women and 5 men.It is needed to find the number of ways a group of these…